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Latest HPCET MSc Physics Exam Question (Objective Questions), MCQ in English
Subjects : Mathematics methods, Classical mechanics and general properties of matter, Optics, Electricity and magnetism, Modern Physics, Nuclear and Particle Physics, Atomic and Molecular, Kinetic Theory of gases and Thermodynamics, Solid State Physics and Electronics
Question Bank HPCET M.Sc. Physics Exam - English
Mathematics methods, Classical mechanics and general properties of matter
Q 1 :
The series Σ (1/n) from n=1 to infinity is:
A.Convergent
B.Divergent
C.Conditionally convergent
D.Absolutely convergent
Q 2 :
The series Σ (1/n²) from n=1 to infinity is:
A.Divergent
B.Convergent
C.Conditionally convergent
D.Oscillatory
Q 3 :
The series Σ (-1)^n / n from n=1 to infinity is:
A.Divergent
B.Absolutely convergent
C.Conditionally convergent
D.Oscillatory
Q 4 :
The series Σ (-1)^n / n² from n=1 to infinity is:
A.Divergent
B.Absolutely convergent
C.Conditionally convergent
D.Oscillatory
Q 5 :
The ratio test for convergence is inconclusive when:
A.Limit of |a(n+1)/a(n)| < 1
B.Limit of |a(n+1)/a(n)| > 1
C.Limit of |a(n+1)/a(n)| = 1
D.Limit of |a(n+1)/a(n)| = 0
Q 6 :
The series Σ (n/2^n) from n=1 to infinity is:
A.Divergent
B.Convergent
C.Conditionally convergent
D.Oscillatory
Q 7 :
The series Σ (1/n!) from n=0 to infinity is:
A.Divergent
B.Convergent
C.Conditionally convergent
D.Oscillatory
Q 8 :
The series Σ (2^n / n!) from n=0 to infinity is:
A.Divergent
B.Convergent
C.Conditionally convergent
D.Oscillatory
Q 9 :
The series Σ (n!) / (n^n) from n=1 to infinity is:
A.Divergent
B.Convergent
C.Conditionally convergent
D.Oscillatory
Q 10 :
The Jacobian of the transformation x = r cos(θ), y = r sin(θ) is:
A.r
B.1/r
C.r²
D.1/r²
Q 11 :
The Taylor expansion of e^x around x=0 is:
A.1 + x + x²/2! + x³/3! + ...
B.1 - x + x²/2! - x³/3! + ...
C.x + x²/2! + x³/3! + ...
D.1 + x + x² + x³ + ...
Q 12 :
If z = f(x, y), then ∂z/∂x represents:
A.Total derivative of z
B.Partial derivative of z with respect to x
C.Partial derivative of z with respect to y
D.Gradient of z
Q 13 :
If f(x, y) = x²y, then ∂²f/∂x∂y is:
A.2x
B.2y
C.x²
D.y²
Q 14 :
If u = x² + y², then ∂u/∂x is:
A.2y
B.2x
C.x + y
D.x - y
Q 15 :
If u = x²y, then ∂u/∂y is:
A.x²
B.2xy
C.y²
D.2x
Q 16 :
If φ is a scalar field, then curl (grad φ) is:
A.grad φ
B.div φ
C.0
D.φ
Q 17 :
The integral ∫∫∫ div F dV over a volume V is equal to:
A.∫∫ F.dS over the surface S enclosing V
B.∫ F.dr along the boundary of V
C.curl F
D.grad F
Q 18 :
The integral ∫ F.dr** along a closed curve C is equal to:**
A.∫∫ curl F.dS over any surface S bounded by C
B.∫∫ div F.dS over any surface S bounded by C
C.grad F
D.div F
Q 19 :
The integral ∫∫ dS over a surface S represents:
A.Volume
B.Area
C.Length
D.Gradient
Q 20 :
The integral ∫∫∫ dV over a volume V represents:
A.Area
B.Volume
C.Length
D.Gradient
Q 21 :
The Laplacian of a scalar field φ is:
A.grad φ
B.div (grad φ)
C.curl φ
D.div φ
Q 22 :
If φ = x² + y² + z², then ∇²φ is:
A.2
B.4
C.6
D.8
Q 23 :
In cylindrical coordinates (ρ, φ, z), the unit vectors are:
A.Constant
B.Vary with ρ
C.Vary with φ
D.Vary with z
Q 24 :
In spherical coordinates (r, θ, φ), the unit vectors are:
A.Constant
B.Vary with r only
C.Vary with θ and φ
D.Vary with z
Q 25 :
The Laplacian operator in spherical coordinates involves derivatives with respect to:
A.r only
B.θ only
C.r, θ, and φ
D.z only
Optics, Electricity and magnetism
Q 26 :
Fermat’s principle states that light travels along the path that takes the:
A.Longest time
B.Shortest time
C.Constant time
D.Average time
Q 27 :
Fermat’s principle is a fundamental principle in:
A.Thermodynamics
B.Electromagnetism
C.Optics
D.Quantum mechanics
Q 28 :
Fermat’s principle can be used to derive the laws of:
A.Thermodynamics
B.Reflection and refraction
C.Quantum mechanics
D.Nuclear physics
Q 29 :
In a homogeneous medium, light travels in a:
A.Curved path
B.Straight line
C.Zigzag path
D.Random path
Q 30 :
When light passes from one medium to another, the path taken minimizes the:
A.Distance
B.Time
C.Velocity
D.Acceleration
Q 31 :
Fermat’s principle is based on the concept of:
A.Energy conservation
B.Momentum conservation
C.Stationary time
D.Charge conservation
Q 32 :
The refractive index of a medium is related to the speed of light in that medium by:
A.n = c/v
B.n = v/c
C.n = cv
D.n = c + v
Q 33 :
Snell’s law of refraction can be derived using:
A.Newton’s laws
B.Fermat’s principle
C.Kirchhoff’s laws
D.Faraday’s law
Q 34 :
The path of light in a gradient-index medium is:
A.Straight
B.Curved
C.Zigzag
D.Random
Q 35 :
The reflection of light from a surface can be explained by Fermat’s principle as:
A.Light taking the longest path
B.Light taking the shortest path
C.Light taking a path of stationary time
D.Light taking any arbitrary path
Q 36 :
A thick lens has a thickness that is:
A.Negligible
B.Significant
C.Zero
D.Variable
Q 37 :
A thin lens has a thickness that is:
A.Significant
B.Negligible
C.Zero
D.Variable
Q 38 :
The lens maker’s formula relates the focal length of a lens to its:
A.Diameter
B.Thickness
C.Radii of curvature and refractive index
D.Object distance
Q 39 :
The power of a lens is the reciprocal of its:
A.Diameter
B.Thickness
C.Focal length
D.Object distance
Q 40 :
The unit of lens power is:
A.Meter (m)
B.Diopter (D)
C.Watt (W)
D.Joule (J)
Q 41 :
The magnification of a lens is the ratio of the:
A.Object distance to image distance
B.Image distance to object distance
C.Object height to image height
D.Image height to object height
Q 42 :
A real image is formed when light rays:
A.Appear to diverge
B.Actually converge
C.Travel in parallel
D.Are absorbed
Q 43 :
A virtual image is formed when light rays:
A.Actually converge
B.Appear to diverge
C.Travel in parallel
D.Are absorbed
Q 44 :
The focal length of a convex lens is:
A.Positive
B.Negative
C.Zero
D.Variable
Q 45 :
The focal length of a concave lens is:
A.Positive
B.Negative
C.Zero
D.Variable
Q 46 :
The principal points of a thick lens are the points where:
A.Light rays converge
B.Light rays diverge
C.Incident and emergent rays have the same direction
D.Light rays are absorbed
Q 47 :
The nodal points of a thick lens are the points where:
A.Light rays converge
B.Light rays diverge
C.Incident and emergent rays are parallel
D.Light rays are absorbed
Q 48 :
The cardinal points of a lens system include:
A.Focal points and principal points
B.Nodal points and principal points
C.Focal points, principal points, and nodal points
D.Object and image points
Q 49 :
The combination of two thin lenses in contact has a power equal to the:
A.Sum of their powers
B.Difference of their powers
C.Product of their powers
D.Ratio of their powers
Q 50 :
The combination of two thin lenses separated by a distance has a power given by:
A.P1 + P2
B.P1 - P2
C.P1 + P2 - dP1P2
D.P1P2
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Modern Physics, Nuclear and Particle Physics
Q 51 :
Inertial frames of reference are those in which:
A.Objects accelerate
B.Objects move with constant velocity or are at rest
C.Objects have variable mass
D.Objects have variable energy
Q 52 :
Galilean invariance states that the laws of mechanics are the same in all:
A.Non-inertial frames
B.Inertial frames
C.Rotating frames
D.Accelerating frames
Q 53 :
The first postulate of special relativity states that the laws of physics are the same in all:
A.Non-inertial frames
B.Inertial frames
C.Rotating frames
D.Accelerating frames
Q 54 :
The second postulate of special relativity states that the speed of light in vacuum is:
A.Variable
B.Constant for all observers
C.Dependent on the observer’s motion
D.Dependent on the source’s motion
Q 55 :
Lorentz transformations are used to relate the coordinates of events in:
A.Non-inertial frames
B.Inertial frames moving relative to each other
C.Rotating frames
D.Accelerating frames
Q 56 :
Length contraction is the phenomenon where the length of an object appears:
A.To increase when moving relative to an observer
B.To decrease when moving relative to an observer
C.To remain the same
D.To vary randomly
Q 57 :
Time dilation is the phenomenon where a moving clock appears to run:
A.Slower than a stationary clock
B.Faster than a stationary clock
C.At the same rate as a stationary clock
D.At a variable rate
Q 58 :
The relativistic velocity addition theorem is used to find the velocity of an object in one frame when its velocity is known in:
A.Non-inertial frames
B.Another inertial frame moving relative to the first
C.Rotating frames
D.Accelerating frames
Q 59 :
Mass-energy equivalence is given by the equation:
A.E = mc
B.E = mc²
C.E = 1/2 mc²
D.E = m²c
Q 60 :
The proper time interval is the time interval measured by an observer:
A.In a moving frame
B.In a stationary frame relative to the event
C.In any frame
D.In a non-inertial frame
Q 61 :
The proper length is the length of an object measured by an observer:
A.In a moving frame
B.In a frame in which the object is at rest
C.In any frame
D.In a non-inertial frame
Q 62 :
The relativistic momentum of a particle is given by:
A.p = mv
B.p = mv
C.p = mv/
D.p = m²v
Q 63 :
The relativistic kinetic energy of a particle is given by:
A.KE = 1/2 mv²
B.KE = mc²
C.KE = ( - 1)mc²
D.KE = mc²/
Q 64 :
The rest mass of a photon is:
A.Non-zero
B.Zero
C.Variable
D.Infinite
Q 65 :
Blackbody radiation is the thermal electromagnetic radiation emitted by:
A.Any object
B.An ideal absorber and emitter
C.A perfect reflector
D.A perfect conductor
Q 66 :
Planck’s law describes the spectral density of blackbody radiation as a function of:
A.Temperature and frequency
B.Temperature and wavelength
C.Temperature, frequency, and wavelength
D.Frequency only
Q 67 :
Rayleigh-Jeans law is a classical approximation for blackbody radiation that works well at:
A.High frequencies
B.Low frequencies
C.All frequencies
D.Intermediate frequencies
Q 68 :
Wien’s law relates the peak wavelength of blackbody radiation to its:
A.Frequency
B.Temperature
C.Intensity
D.Energy
Q 69 :
The photoelectric effect is the emission of electrons from a metal surface when it is illuminated by:
A.Heat
B.Light
C.Magnetic field
D.Electric field
Q 70 :
The stopping potential in the photoelectric effect is a measure of the maximum kinetic energy of the:
A.Incident photons
B.Emitted electrons
C.Metal atoms
D.Metal ions
Q 71 :
The work function of a metal is the minimum energy required to:
A.Ionize the metal
B.Emit an electron from the metal surface
C.Heat the metal
D.Magnetize the metal
Q 72 :
The Compton effect is the scattering of:
A.Electrons by photons
B.Photons by electrons
C.Protons by photons
D.Photons by protons
Q 73 :
In the Compton effect, the wavelength of the scattered photon is:
A.Longer than the incident photon
B.Shorter than the incident photon
C.The same as the incident photon
D.Variable
Q 74 :
The Compton shift depends on the scattering angle and the:
A.Intensity of the incident photon
B.Frequency of the incident photon
C.Wavelength of the incident photon
D.Energy of the incident photon
Q 75 :
Planck’s constant (h) has the units of:
A.Joules
B.Watts
C.Joule-seconds
D.Volts
Atomic and Molecular, Kinetic Theory of gases and Thermodynamics, Solid State Physics and Electronics
Q 76 :
Good quantum numbers for an atom include:
A.n, l, m_l, s
B.n, l, m_l, m_s
C.n, l, j, m_j
D.All of the above
Q 77 :
Fine structure in atomic spectra is due to:
A.Spin-orbit coupling
B.Nuclear spin
C.Doppler effect
D.Zeeman effect
Q 78 :
The Landé g-factor is used to calculate the:
A.Electric dipole moment
B.Magnetic dipole moment
C.Electric quadrupole moment
D.Nuclear spin
Q 79 :
Space quantization refers to the quantization of:
A.Energy
B.Momentum
C.Angular momentum orientation
D.Spin
Q 80 :
The Zeeman effect is the splitting of spectral lines in a:
A.Gravitational field
B.Electric field
C.Magnetic field
D.Thermal gradient
Q 81 :
The Pauli exclusion principle states that no two electrons can have the same set of:
A.Energy levels
B.Quantum numbers
C.Positions
D.Momenta
Q 82 :
Hund’s rule states that the ground state of an atom has the maximum value of:
A.Orbital angular momentum (L)
B.Spin angular momentum (S)
C.Total angular momentum (J)
D.Both a and b
Q 83 :
The spectroscopic term symbol for a many-electron atom is written as:
A.2S+1L_J
B.2L+1S_J
C.L_J^(2S+1)
D.S_J^(2L+1)
Q 84 :
The spectra of alkali atoms are similar to that of:
A.Helium
B.Hydrogen
C.Nitrogen
D.Oxygen
Q 85 :
Alkaline earth atoms have spectra with:
A.Singlet and triplet states
B.Only singlet states
C.Only triplet states
D.No spectral lines
Q 86 :
The selection rule for the azimuthal quantum number (l) is:
A.l = 0
B.l = ±1
C.l = ±2
D.l = any integer
Q 87 :
The selection rule for the magnetic quantum number (m_j) is:
A.m_j = 0
B.m_j = ±1
C.m_j = 0, ±1
D.m_j = any integer
Q 88 :
Raman effect involves the scattering of:
A.Electrons
B.Neutrons
C.Photons
D.Protons
Q 89 :
Stokes lines in Raman spectra correspond to:
A.Energy gain by the molecule
B.Energy loss by the molecule
C.No energy change
D.Nuclear spin change
Q 90 :
Anti-Stokes lines in Raman spectra correspond to:
A.Energy gain by the molecule
B.Energy loss by the molecule
C.No energy change
D.Nuclear spin change
Q 91 :
Raman and infrared spectroscopy are complementary because they probe:
A.Same vibrational modes
B.Different vibrational modes
C.Rotational modes
D.Electronic transitions
Q 92 :
Infrared spectroscopy is sensitive to changes in:
A.Polarizability
B.Dipole moment
C.Nuclear spin
D.Electronic configuration
Q 93 :
Raman spectroscopy is sensitive to changes in:
A.Polarizability
B.Dipole moment
C.Nuclear spin
D.Electronic configuration
Q 94 :
The selection rule for rotational transitions in a diatomic molecule is:
A.J = 0
B.J = ±1
C.J = ±2
D.J = any integer
Q 95 :
The vibrational energy levels of a diatomic molecule are modeled using the:
A.Rigid rotor model
B.Harmonic oscillator model
C.Free particle model
D.Nuclear shell model
Q 96 :
The rotational constant (B) is inversely proportional to the:
A.Reduced mass
B.Moment of inertia
C.Both a and b
D.Vibrational frequency
Q 97 :
The vibrational frequency is proportional to the square root of the:
A.Reduced mass
B.Force constant
C.Both a and b
D.Moment of inertia
Q 98 :
The anharmonicity constant accounts for the:
A.Deviation from the rigid rotor model
B.Deviation from the harmonic oscillator model
C.Spin-orbit coupling
D.Zeeman effect
Q 99 :
The centrifugal distortion constant accounts for the:
A.Deviation from the rigid rotor model
B.Deviation from the harmonic oscillator model
C.Spin-orbit coupling
D.Zeeman effect
Q 100 :
The pure rotational spectrum of a diatomic molecule lies in the:
